Umbilical cord blood is potentially a rich resource of primitive hematopoietic cells for transplantation into patients who need a bone marrow transplant but lack an appropriate donor, such as selected patients with acute and chronic leukemia, lymphoma, or neuroblastoma. One method of identification of primitive hematopoietic cells is the presence of the CD34 antigen on the cell surface. This protocol will investigate the optimal method of expanding CD34+ blood cells and will study the efficacy of gene transfer methods into CD34+ cord blood cells.